11/26/2007

Kenji Nakanishi
Kyoto University

Unconditional uniqueness for Zakharov systems

This is joint work with Nader Masmoudi. We prove uniqueness of weak solutions in the energy space for the Klein-Gordon-Zakharov system, and in the space with half regularity for the Zakharov system. The latter seems particularly nontrivial, beacuse the regularity is the scaling critical for the subsonic limit, the nonlinear Schrodinger equation. The local wellposedness was proved in the so-called X^{s,b} spaces with the above regularity for the former system by Ozawa, Tsutaya, and Tsutsumi, and for the latter by Ginibre, Tsutsumi and Velo. We prove that bounds in the data space is sufficient to recover those X^{s,b} spaces. Our proof uses the iteration, where the solution is fixed but the function space converges to the desired one.